Z axis of mapping node in Shader is not working
It's moving but you can't see it because the projection is flat, it means that the image is only projected on the object local Z axis and therefore on the side you'll only see the stretched pixels of the picture. If in the Image Texture you choose Box instead of Flat you'll see the texture projected on the sides and you'll be able to move it.



But keep in mind that even with the Box option, if you rotate your image, it will stretch it. It's not because it is projected on its face that it can't be stretched if you rotate it.